B7.3.1 · Strand 3, sub-strand 1

Shape and Space

Measuring and classifying angles, angle facts, and compass-and-ruler constructions.

1. Lesson 1 · B7.3.1.1.1 · about 45 min

   Measuring and Classifying Angles

   Angles are everywhere: the corner of your exercise book, the opening of a gate, the hands of a clock and the slope of a roof. In this lesson you will learn to name every kind of angle, measure angles accurately with a protractor, and draw angles of a given size, including the big ones larger than 180°.

2. Lesson 2 · B7.3.1.1.2 · about 45 min

   Complementary and Supplementary Angles

   Some angles come in pairs that fit together perfectly: two angles that fill a corner, or two that fill a straight line. Carpenters, tailors and builders in every Ghanaian town use these pairs to cut wood and cloth neatly. In this lesson you will learn the two special pairs, complementary and supplementary angles, and use them to find missing angles.

3. Lesson 3 · B7.3.1.1.3 · about 45 min

   Adjacent, Supplementary and Vertically Opposite Angles

   When two straight lines cross, like two roads at a roundabout or the blades of a pair of scissors, four angles are made. They are not random: they follow neat rules. In this lesson you will learn the names of the angle pairs, the three key facts about angles on a line, at a point and between crossing lines, and use them to find missing angles.

4. Lesson 4 · B7.3.1.2.1 · about 50 min

   Constructing Perpendicular Lines with Compasses and Ruler

   A builder checking that a wall stands straight, a farmer marking rows at right angles to a path, and a surveyor setting out a plot all need perpendicular lines. In this lesson you will use only a pair of compasses and a ruler to copy a line segment, draw a perpendicular at a point on a line, and drop a perpendicular from a point outside a line.

5. Lesson 5 · B7.3.1.2.2 · about 45 min

   Constructing the Perpendicular Bisector of a Line Segment

   A fair cut must go through the exact middle, whether you are sharing bread, placing a borehole between two villages or finding the centre of a round table. In this lesson you will use only compasses and a ruler to cut a line in half at 90°, and you will learn why the method works.

6. Lesson 6 · B7.3.1.2.3 · about 45 min

   Copying and Bisecting Angles

   Carpenters, tailors and welders constantly need to repeat an angle exactly, or to cut it into two equal halves. In this lesson you will learn the compass-and-ruler methods for copying and bisecting an angle, understand why they work, and use them to solve problems.

7. Lesson 7 · B7.3.1.2.4 · about 45 min

   Constructing Angles of 90° and 45°

   Every square corner in a building, every set square in your geometry box and every mitred picture frame depends on the right angle (90°) and on 45°. In this lesson you will build both with compasses and a ruler, so that you understand how they are made and can check them.

8. Lesson 8 · B7.3.1.2.5 · about 45 min

   Constructing Angles of 60° and 30°

   The 60° angle is the easiest angle to construct, and it opens the door to many others. A 30° angle is simply half of 60°. In this lesson you will use compasses and a ruler to construct both, see why the 60° method works, and use the angles in problems.

9. Lesson 9 · B7.3.1.2.6 · about 45 min

   Constructing Angles of 15° and 75°

   Once you can make 60°, 90° and bisect an angle, a whole family of angles opens up. In this lesson you will use bisecting and adding to construct 15° and 75°, and you will learn to plan a route before you pick up your compasses.

10. Lesson 10 · B7.3.1.2.7 · about 40 min

    Perpendiculars and Bisectors in the Environment

    Right angles, midpoints and equal halves are not just ideas from your geometry set. They hold up buildings, shape roofs, fix electricity poles and mark out a football pitch. In this lesson you will find perpendicular lines, perpendicular bisectors and angle bisectors in the world around you, and practise estimating angles.